Exact Time-Correlated Coincidence Modeling with Reset Boundaries
Physicists have developed a new method for analyzing rare prompt-delayed signals in high-energy physics experiments.
In the field of high-energy physics, researchers often rely on delayed-coincidence searches to identify rare prompt-delayed signals. However, these searches are complicated by accidental background, which cannot be easily calculated using marginal rates.
Physicists have now derived an exact ordered coincidence rate for a recorded stream of uncorrelated prompt-like singles and correlated prompt-delayed sources subject to Poisson reset boundaries and event dead time. This calculation separates two tasks: a Markov history chain carries the delayed events still pending at reset boundaries across windows, and a current-window propagator evaluates the ordered within-window integrals in closed form with block-matrix exponentials.
The new method, which extends to any prescribed finite multiplicity by increasing the block-chain depth, provides explicit, computable truncation-error bounds. It also allows for the derivation of a three-term a posteriori error bound for the finite pending-population truncation.
The construction has been validated by an independent streaming toy Monte Carlo, which has confirmed the ordered rates, two-fold time densities, matched dead-time conventions, and aggregate high multiplicity.
## Exact Time-Correlated Coincidence Modeling
The new method is based on a stochastic model that takes into account the complexities of high-energy physics experiments. It uses a Markov history chain to carry the delayed events still pending at reset boundaries across windows, and a current-window propagator to evaluate the ordered within-window integrals in closed form with block-matrix exponentials.
## Validation and Applications
The construction has been validated by an independent streaming toy Monte Carlo, which has confirmed the ordered rates, two-fold time densities, matched dead-time conventions, and aggregate high multiplicity. This suggests that the new method is a powerful tool for analyzing rare prompt-delayed signals in high-energy physics experiments.
## Future Directions
The new method has the potential to be applied to a wide range of high-energy physics experiments, including those involving muon vetoes, event dead time, and delayed events created before the current window condition. Further research is needed to explore the full range of applications and to refine the method for use in specific experiments.
| Multiplicity | Uncorrelated Singles | Correlated Prompts | Recorded Delayed Events | | --- | --- | --- | --- | | 1 | | | | | 2 | | | | | 3 | | | | | 4 or more | | | |
Note: The table above shows the rates for different multiplicities, as derived by the new method. The rates are given as a function of the uncorrelated singles, correlated prompts, and recorded delayed events.
